Average Error: 5.7 → 2.2
Time: 21.0s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.1240441509892456 \cdot 10^{-20}:\\ \;\;\;\;\left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right) + t \cdot \left(x \cdot \left(z \cdot \left(18.0 \cdot y\right)\right) - a \cdot 4.0\right)\\ \mathbf{elif}\;t \le 1.0458702014704218 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - \left(j \cdot \left(27.0 \cdot k\right) + 4.0 \cdot \left(x \cdot i\right)\right)\right) + \left(18.0 \cdot \left(\left(z \cdot \left(x \cdot t\right)\right) \cdot y\right) - \left(t \cdot a\right) \cdot 4.0\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t} \cdot \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right)\right) + \left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right)\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.1240441509892456 \cdot 10^{-20}:\\
\;\;\;\;\left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right) + t \cdot \left(x \cdot \left(z \cdot \left(18.0 \cdot y\right)\right) - a \cdot 4.0\right)\\

\mathbf{elif}\;t \le 1.0458702014704218 \cdot 10^{+56}:\\
\;\;\;\;\left(b \cdot c - \left(j \cdot \left(27.0 \cdot k\right) + 4.0 \cdot \left(x \cdot i\right)\right)\right) + \left(18.0 \cdot \left(\left(z \cdot \left(x \cdot t\right)\right) \cdot y\right) - \left(t \cdot a\right) \cdot 4.0\right)\\

\mathbf{else}:\\
\;\;\;\;\sqrt[3]{t} \cdot \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right)\right) + \left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r2142486 = x;
        double r2142487 = 18.0;
        double r2142488 = r2142486 * r2142487;
        double r2142489 = y;
        double r2142490 = r2142488 * r2142489;
        double r2142491 = z;
        double r2142492 = r2142490 * r2142491;
        double r2142493 = t;
        double r2142494 = r2142492 * r2142493;
        double r2142495 = a;
        double r2142496 = 4.0;
        double r2142497 = r2142495 * r2142496;
        double r2142498 = r2142497 * r2142493;
        double r2142499 = r2142494 - r2142498;
        double r2142500 = b;
        double r2142501 = c;
        double r2142502 = r2142500 * r2142501;
        double r2142503 = r2142499 + r2142502;
        double r2142504 = r2142486 * r2142496;
        double r2142505 = i;
        double r2142506 = r2142504 * r2142505;
        double r2142507 = r2142503 - r2142506;
        double r2142508 = j;
        double r2142509 = 27.0;
        double r2142510 = r2142508 * r2142509;
        double r2142511 = k;
        double r2142512 = r2142510 * r2142511;
        double r2142513 = r2142507 - r2142512;
        return r2142513;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r2142514 = t;
        double r2142515 = -3.1240441509892456e-20;
        bool r2142516 = r2142514 <= r2142515;
        double r2142517 = b;
        double r2142518 = c;
        double r2142519 = r2142517 * r2142518;
        double r2142520 = 4.0;
        double r2142521 = x;
        double r2142522 = i;
        double r2142523 = r2142521 * r2142522;
        double r2142524 = r2142520 * r2142523;
        double r2142525 = 27.0;
        double r2142526 = j;
        double r2142527 = r2142525 * r2142526;
        double r2142528 = k;
        double r2142529 = r2142527 * r2142528;
        double r2142530 = r2142524 + r2142529;
        double r2142531 = r2142519 - r2142530;
        double r2142532 = z;
        double r2142533 = 18.0;
        double r2142534 = y;
        double r2142535 = r2142533 * r2142534;
        double r2142536 = r2142532 * r2142535;
        double r2142537 = r2142521 * r2142536;
        double r2142538 = a;
        double r2142539 = r2142538 * r2142520;
        double r2142540 = r2142537 - r2142539;
        double r2142541 = r2142514 * r2142540;
        double r2142542 = r2142531 + r2142541;
        double r2142543 = 1.0458702014704218e+56;
        bool r2142544 = r2142514 <= r2142543;
        double r2142545 = r2142525 * r2142528;
        double r2142546 = r2142526 * r2142545;
        double r2142547 = r2142546 + r2142524;
        double r2142548 = r2142519 - r2142547;
        double r2142549 = r2142521 * r2142514;
        double r2142550 = r2142532 * r2142549;
        double r2142551 = r2142550 * r2142534;
        double r2142552 = r2142533 * r2142551;
        double r2142553 = r2142514 * r2142538;
        double r2142554 = r2142553 * r2142520;
        double r2142555 = r2142552 - r2142554;
        double r2142556 = r2142548 + r2142555;
        double r2142557 = cbrt(r2142514);
        double r2142558 = r2142557 * r2142557;
        double r2142559 = r2142521 * r2142534;
        double r2142560 = r2142532 * r2142533;
        double r2142561 = r2142559 * r2142560;
        double r2142562 = r2142561 - r2142539;
        double r2142563 = r2142558 * r2142562;
        double r2142564 = r2142557 * r2142563;
        double r2142565 = r2142564 + r2142531;
        double r2142566 = r2142544 ? r2142556 : r2142565;
        double r2142567 = r2142516 ? r2142542 : r2142566;
        return r2142567;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Bits error versus j

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if t < -3.1240441509892456e-20

    1. Initial program 2.4

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Simplified2.4

      \[\leadsto \color{blue}{\left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot t}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity2.4

      \[\leadsto \left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot \color{blue}{\left(1 \cdot t\right)}\]

    5. Applied associate-*r*2.4

      \[\leadsto \left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \color{blue}{\left(\left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot 1\right) \cdot t}\]

    6. Simplified2.3

      \[\leadsto \left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \color{blue}{\left(x \cdot \left(z \cdot \left(18.0 \cdot y\right)\right) - 4.0 \cdot a\right)} \cdot t\]

    if -3.1240441509892456e-20 < t < 1.0458702014704218e+56

    1. Initial program 7.5

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Simplified7.4

      \[\leadsto \color{blue}{\left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot t}\]

    3. Taylor expanded around inf 7.7

      \[\leadsto \left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \color{blue}{\left(18.0 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right) - 4.0 \cdot \left(t \cdot a\right)\right)}\]
    4. Using strategy rm

    5. Applied associate-*r*5.4

      \[\leadsto \left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \left(18.0 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot y\right)\right)} - 4.0 \cdot \left(t \cdot a\right)\right)\]
    6. Using strategy rm

    7. Applied associate-*r*2.0

      \[\leadsto \left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \left(18.0 \cdot \color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right)} - 4.0 \cdot \left(t \cdot a\right)\right)\]
    8. Using strategy rm

    9. Applied associate-*r*2.1

      \[\leadsto \left(b \cdot c - \left(\color{blue}{\left(k \cdot 27.0\right) \cdot j} + \left(x \cdot i\right) \cdot 4.0\right)\right) + \left(18.0 \cdot \left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right) - 4.0 \cdot \left(t \cdot a\right)\right)\]

    if 1.0458702014704218e+56 < t

    1. Initial program 1.9

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Simplified1.9

      \[\leadsto \color{blue}{\left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot t}\]
    3. Using strategy rm

    4. Applied add-cube-cbrt2.5

      \[\leadsto \left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\]

    5. Applied associate-*r*2.5

      \[\leadsto \left(b \cdot c - \left(k \cdot \left(27.0 \cdot j\right) + \left(x \cdot i\right) \cdot 4.0\right)\right) + \color{blue}{\left(\left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.1240441509892456 \cdot 10^{-20}:\\ \;\;\;\;\left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right) + t \cdot \left(x \cdot \left(z \cdot \left(18.0 \cdot y\right)\right) - a \cdot 4.0\right)\\ \mathbf{elif}\;t \le 1.0458702014704218 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - \left(j \cdot \left(27.0 \cdot k\right) + 4.0 \cdot \left(x \cdot i\right)\right)\right) + \left(18.0 \cdot \left(\left(z \cdot \left(x \cdot t\right)\right) \cdot y\right) - \left(t \cdot a\right) \cdot 4.0\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t} \cdot \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(x \cdot y\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right)\right) + \left(b \cdot c - \left(4.0 \cdot \left(x \cdot i\right) + \left(27.0 \cdot j\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))